Bill,
I work with Tru Oil ALL the time.
First thing is raid the wife’s or girlfriend’s supply of Q tips for about a half dozen of them. Sounds like with your avatar, you might get some at work.
Dip one end in acetone and squeeze it out so the tip is damp, but not wet. Lightly swipe over the oil at first to maybe having to apply a little pressure on it. As the ends get dirty, use a new end that is damp with acetone. This will quickly knock off the shine without damaging the finish or anything else around it.
Gus